Averaging methods for transient regimes in overloading retrial queueing systems

Authors:
V. V. Anisimov
Affiliations:
Department of Industrial Engineering Bilkent University, Ankara, Turkey and Applied Statistics Department Kiev University, Kiev, Ukraine
Venue:
Mathematical and Computer Modelling: An International Journal
Year:
1999

Citing 3
Cited 5

A survey of retrial queues

Queueing Systems: Theory and Applications - Special issue of queueing systems, theory and applications
Retrial queues revisited

Frontiers in queueing
Analysis of an M/G/1 queue with constant repeated attempts and server vacations

Computers and Operations Research

Some Markovian Queuing Retrial Systems under Light-Traffic Conditions

Cybernetics and Systems Analysis
Analysis of Markov Multiserver Retrial Queues with Negative Arrivals

Queueing Systems: Theory and Applications
Diffusion Approximation in Overloaded Switching Queueing Models

Queueing Systems: Theory and Applications
A Retrial BMAP/PH/N System

Queueing Systems: Theory and Applications
Switching queueing networks

Network performance engineering

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Abstract

A new approach is suggested to study transient and stable regimes in overloading retrial queueing systems. This approach is based on limit theorems of averaging principle and diffusion approximation types for so-called switching processes. Two models of retrial queueing systems of the types M@?/G@?/1@?/w.r (multidimensional Poisson input flow, one server with general service times, retrial system) and M/M/m/w.r (m servers with exponential service) are considered in the case when the intensity of calls that reapply for the service tends to zero. For the number of re-applying calls, functional limit theorems of averaging principle and diffusion approximation types are proved.